NURBS interpolator with confined chord error and tangential and centripetal acceleration control

NURBS interpolation is highly requested in CNC systems because it allows high speed and high accuracy machining. In this work, an algorithm for NURBS interpolation capable of limiting chord error, centripetal acceleration and tangential acceleration is proposed. The algorithm is composed of two stages that may be executed simultaneously. In the first stage, the algorithm breaks down the curve into segments and, for each segment, calculates the feedrate limit that allows to respect both chord error tolerance and maximum centripetal acceleration limit. The second stage is a speed-controlled interpolator with a tangential acceleration limited feedrate profile generated using information provided by first stage. Software simulations are performed to verify the fulfillment of constraints and performance is compared to those of speed-controlled interpolator and variable feedrate interpolator.